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Enginius/Machine Learning

Laplace Approximation

Laplace's method
From Wikipedia, the free encyclopedia

In mathematicsLaplace's method, named after Pierre-Simon Laplace, is a technique used to approximate integrals of the form

 \int_a^b\! e^{M f(x)} \, dx

where ƒ(x) is some twice-differentiable functionM is a large number, and the integral endpoints aand b could possibly be infinite. This technique was originally presented in Laplace (1774, pp. 366–367).

\int_a^b\! e^{M f(x)}\, dx\approx \sqrt{\frac{2\pi}{M|f''(x_0)|}}e^{M f(x_0)}  \mbox { as } M\to\infty. \,


 

 관련 논문과 발표 자료 

1. accurate approximations for posterior moments and marginal densities.pdf

2. fully exponential laplace approximations to Expectations and Variances of Nonpositive Functions.pdf

3. Laplace’s Method Approximations for Probabilistic Inference in Belief Networks with Continuous Variables.pdf

4. fully exponential laplace approximations using asymptotic modes.pdf

Laplace Approximation.pptx


 정리한 것 SCAN 











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